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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 769, page id 1815201908:0826
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vet
11
EN P L A N V H.
eROPOSTTIOK
Irculum ABF secet recta quaedam AB non per centru ducta;
sactilque per A _ B orrhogonis C AE, DBF, hac Cuper AB rectan
sulum ACDB: _ HIOL rectangulis aequalia ponantur rectangula
LCIE: Facile colligicur ex illis que in libro de parabola demonstraui, pun-
Ct2 R IS ehe ad parabolam.
Dico G FI ductum in K L aequari FII ductoin CR.
Demonstratio.
)Veaneur insinitx GHLKL
Parallelae ad C AF, DBF.
Ouoniam TC K rectagula a qua-
lia ponuncur rectangulis FTCFL,
eric ve GTI ad GI, BCGR ad 1.
GL; & diuidendo ve GHI ad FIL,
sC GK ad KL: vnde TITOK
rectangulis aequalia (uNE FCCTaN- L
sula OTTKL. ergo CTI du. 5
CEUM In KF. 2 x9ual0 FII duCtO
in GR. Ouod Fuic demonstran.
dum.
PROPOSI)
NIrculum BC contingant dux parallelx F G, TIl quas orthogonali-
scer lecerin F _ HI linea A A; hanrque B A C rectangulis aequalia re-
CTanSULA DAF. (INE AUTEMDD, E. F sectiones opposr quarum cen-
EFUM GIEIAROCEA A A.
DicoD A planum duccum in planum BF. xquari AB ducrO in L. C.
Demonstratio.
Vonia B AC ECCLatBS a
Lqualia ponuneur rectangula
D AF, AF duccum insc, b xquale
est AB ductO in A C. scd A B duccu
in AC aquatuE AB ducro in AF,
_ AB ducroin F C: icem AF du-
etum in se, siue D A duccum in A V.
RQUAEUE D A SInC F A duccO in AB,
via cum D A ducto in B E; dempto
isicur communi F A ducco in AB,
remanebie D A duccum in BF. X-
quale AB dueco in F. C. Quodtuie
demonstrandum.
2
XCVII.
962
EcccC
B 45. hains
 e te  ete   et e ti e t e t t   e tte te tat  t t t  a e t  t t t   A te